Both players appealed their punishment and will remain eligible to play until the matter is resolved.
Royals manager Trey Hillman was suspended one game and was to serve it during Tuesday night's game against the Boston Red Sox. Hillman had no right of appeal, he said.
White Sox manager Ozzie Guillen was suspended for two games for "aggressive actions," which included making contact with umpire Tim Timmons after a fifth-inning ruckus, and for comments after the game. Guillen was to serve his two games starting Tuesday night against the Detroit Tigers.
No White Sox players were penalized, although pitcher D.J. Carrasco's pitches, the third of which struck Olivo, ignited a bench-clearing brouhaha in the fifth inning. Olivo charged the mound but was restrained by White Sox catcher A.J. Pierzynski before reaching Carrasco as the benches cleared. Later in the scrum, Olivo was seen throwing a punch, apparently at Pierzysnki.
The four suspensions each included a fine -- Greinke said he believed his was for $1,500 -- and were announced Tuesday afternoon by Bob Watson, vice president of on-field operations for Major League Baseball.
"When I heard that [Carrasco] did not get suspended at all, I was disappointed, because I'm hurt," Olivo said. "I got my left hand hurt and my right hand hurt. I didn't agree.
"I knew I would get suspended, but not like five days -- maybe three or two games. I agree with that, but five games is a lot."
Olivo actually was hit twice by Carrasco. One pitch glanced off his bat for a foul that hit his left hand. Carrasco's third pitch hit the right hand. After the scuffle, Olivo and Carrasco were ejected. Guillen was thumbed shortly thereafter.
Greinke was suspended "for intentionally throwing at a batter" in the seventh inning after both benches had been warned following the Carrasco-Olivo incident.
Greinke reiterated that he did not throw intentionally at Nick Swisher, who was struck by a pitch in the hip. But Greinke observed that no pitcher would admit throwing at a hitter so MLB has to make that judgment.
"And you've got to be a better pitcher than that," Greinke said. You've got to avoid hitting a batter when you know you've been warned."
Hillman was asked how MLB could determine intent.
"How can they say unintentionally for Carrasco, when he gets nothing?" he said.
Asked what he really thought, Hillman replied: "[I] can't answer it. I can tell you a lot about what I think, but I won't. Major League Baseball doesn't want us airing our dirty laundry through the print and the media and we're going to adhere to that."
Greinke wasn't too surprised that Carrasco went unpunished. In the aftermath of a Runelvys Hernandez-Tigers brouhaha in 2005, Greinke recalled being ejected in a later game for hitting Ivan Rodriguez with a pitch. Because there was no warning issued beforehand, he was not suspended.
In Chicago, the White Sox insisted that Carrasco was not aiming at Olivo.
"Like I said, no one was throwing at anybody. We weren't trying to hit anybody," Pierzynski said. "The bases were loaded and we were down six or seven runs. It's idiotic for anyone to think that."
Hillman had to get out of uniform after Tuesday's batting practice to serve his suspension. He was permitted to join general manager Dayton Moore in his upstairs suite but wasn't sure he could sit still that long.
"I'll probably be pacing up and down the stairs," he said.
As for Olivo, he had no regrets.
"I think I did what I needed to do," he said. "I don't know whether they did it on purpose or not."
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.